@article { author = {Nezhadhosein, Saeed and Mohammadkhan Sartip, Sahar}, title = {Two Settings of the Dai-Liao Parameter Based on Modified Secant Equations}, journal = {Control and Optimization in Applied Mathematics}, volume = {3}, number = {2}, pages = {59-76}, year = {2018}, publisher = {Payame Noor University (PNU)}, issn = {2383-3130}, eissn = {2538-5615}, doi = {10.30473/coam.2020.46435.1116}, abstract = {Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hestenes-Stiefel CG method‎. ‎The second is based on the quasi-Newton (QN) approach‎. ‎Global convergence of the proposed methods for uniformly convex functions and general functions is proved‎. ‎Numerical experiments are done on a set of test functions of the CUTEr collection and the results are compared with some well-known methods.}, keywords = {Unconstrained optimization‎,‎Modified secant equations‎,‎Dai-Liao conjugate gradient method}, url = {https://mathco.journals.pnu.ac.ir/article_6722.html}, eprint = {https://mathco.journals.pnu.ac.ir/article_6722_a305748baa33534bbbd3520c72a3b261.pdf} }